Application to the proximal point algorithm to the general traffic assignment problem

Abstract

An adaptation of the proximal algorithm for the traffic assignment problem under a user equilibrium formulation for a general asymmetric traffic network is presented in this paper, following the recently published results of Pennanen regarding convergence under nonmonotonicity. As is well known the problem can be formulated as a variational inequality and the algorithmic solutions developed uptodate guarantee convergence only under too restrictive conditions which are difficult to appear in practice. In this paper new conditions guaranteing convergence are developed and the possibility of including the algorithm on a bilevel scheme is discussed